172,748 research outputs found
Avalanches and rate effects in strain-controlled discrete dislocation plasticity of Al single crystals
Three-dimensional discrete dislocation dynamics simulations are used to study
strain-controlled plastic deformation of face-centered cubic aluminium single
crystals. After describing the rate and size dependence of the average
stress-strain curves, we study the power-law distributed strain bursts and the
average avalanche shapes, and find a universal power-law exponent for all imposed strain rates and system sizes, characterizing both the
event sizes and their durations. We discuss the dependence of our results on
loading rate and compare these with previous studies of strain-controlled
two-dimensional systems of discrete dislocations as well as of quasistatic
stress-controlled loading of aluminium single crystals.Comment: 7 pages, 6 figures, 39 citation
The role of initial geometry in experimental models of wound closing
Wound healing assays are commonly used to study how populations of cells,
initialised on a two-dimensional surface, act to close an artificial wound
space. While real wounds have different shapes, standard wound healing assays
often deal with just one simple wound shape, and it is unclear whether varying
the wound shape might impact how we interpret results from these experiments.
In this work, we describe a new kind of wound healing assay, called a sticker
assay, that allows us to examine the role of wound shape in a series of wound
healing assays performed with fibroblast cells. In particular, we show how to
use the sticker assay to examine wound healing with square, circular and
triangular shaped wounds. We take a standard approach and report measurements
of the size of the wound as a function of time. This shows that the rate of
wound closure depends on the initial wound shape. This result is interesting
because the only aspect of the assay that we change is the initial wound shape,
and the reason for the different rate of wound closure is unclear. To provide
more insight into the experimental observations we describe our results
quantitatively by calibrating a mathematical model, describing the relevant
transport phenomena, to match our experimental data. Overall, our results
suggest that the rates of cell motility and cell proliferation from different
initial wound shapes are approximately the same, implying that the differences
we observe in the wound closure rate are consistent with a fairly typical
mathematical model of wound healing. Our results imply that parameter estimates
obtained from an experiment performed with one particular wound shape could be
used to describe an experiment performed with a different shape. This
fundamental result is important because this assumption is often invoked, but
never tested
On the critical nature of plastic flow: one and two dimensional models
Steady state plastic flows have been compared to developed turbulence because
the two phenomena share the inherent complexity of particle trajectories, the
scale free spatial patterns and the power law statistics of fluctuations. The
origin of the apparently chaotic and at the same time highly correlated
microscopic response in plasticity remains hidden behind conventional
engineering models which are based on smooth fitting functions. To regain
access to fluctuations, we study in this paper a minimal mesoscopic model whose
goal is to elucidate the origin of scale free behavior in plasticity. We limit
our description to fcc type crystals and leave out both temperature and rate
effects. We provide simple illustrations of the fact that complexity in rate
independent athermal plastic flows is due to marginal stability of the
underlying elastic system. Our conclusions are based on a reduction of an
over-damped visco-elasticity problem for a system with a rugged elastic energy
landscape to an integer valued automaton. We start with an overdamped one
dimensional model and show that it reproduces the main macroscopic
phenomenology of rate independent plastic behavior but falls short of
generating self similar structure of fluctuations. We then provide evidence
that a two dimensional model is already adequate for describing power law
statistics of avalanches and fractal character of dislocation patterning. In
addition to capturing experimentally measured critical exponents, the proposed
minimal model shows finite size scaling collapse and generates realistic shape
functions in the scaling laws.Comment: 72 pages, 40 Figures, International Journal of Engineering Science
for the special issue in honor of Victor Berdichevsky, 201
Fission-fragment mass distributions from strongly damped shape evolution
Random walks on five-dimensional potential-energy surfaces were recently
found to yield fission-fragment mass distributions that are in remarkable
agreement with experimental data. Within the framework of the Smoluchowski
equation of motion, which is appropriate for highly dissipative evolutions, we
discuss the physical justification for that treatment and investigate the
sensitivity of the resulting mass yields to a variety of model ingredients,
including in particular the dimensionality and discretization of the shape
space and the structure of the dissipation tensor. The mass yields are found to
be relatively robust, suggesting that the simple random walk presents a useful
calculational tool. Quantitatively refined results can be obtained by including
physically plausible forms of the dissipation, which amounts to simulating the
Brownian shape motion in an anisotropic medium.Comment: 14 pages, 11 ps figure
Multicritical continuous random trees
We introduce generalizations of Aldous' Brownian Continuous Random Tree as
scaling limits for multicritical models of discrete trees. These discrete
models involve trees with fine-tuned vertex-dependent weights ensuring a k-th
root singularity in their generating function. The scaling limit involves
continuous trees with branching points of order up to k+1. We derive explicit
integral representations for the average profile of this k-th order
multicritical continuous random tree, as well as for its history distributions
measuring multi-point correlations. The latter distributions involve
non-positive universal weights at the branching points together with fractional
derivative couplings. We prove universality by rederiving the same results
within a purely continuous axiomatic approach based on the resolution of a set
of consistency relations for the multi-point correlations. The average profile
is shown to obey a fractional differential equation whose solution involves
hypergeometric functions and matches the integral formula of the discrete
approach.Comment: 34 pages, 12 figures, uses lanlmac, hyperbasics, eps
Cracks and fingers: dynamics of ductile fracture in an aqueous foam
Fracture of a quasi-two-dimensional aqueous foam by injection of air can occur via two distinct mechanisms, termed brittle and ductile, which are analogous to crack modes observed for crystalline atomic solids such as metals. In the present work we focus on the dynamics and morphology of the ductile process, in which no films between bubbles are broken. A network modeling approach allows detailed analysis of the foam morphology from individual bubbles to the shape of the propagating crack. This crack develops similarly to fingering instabilities in Hele–Shaw cells filled with homogeneous fluids. We show that the observed width and shape of the crack are compatible this interpretation, and that the discreteness of the bubble structure provides symmetry perturbations and limiting scales characteristic of anomalous fingering. The model thus bridges the gap between fracture of the solid foam lattice and instability growth of interfaces in a fluid system
Models of collective cell motion for cell populations with different aspect ratio: diffusion, proliferation & travelling waves
Continuum, partial differential equation models are often used to describe the collective motion of cell populations, with various types of motility represented by the choice of diffusion coefficient, and cell proliferation captured by the source terms. Previously, the choice of diffusion coefficient has been largely arbitrary, with the decision to choose a particular linear or nonlinear form generally based on calibration arguments rather than making any physical connection with the underlying individual-level properties of the cell motility mechanism. In this work we provide a new link between individual-level models, which account for important cell properties such as varying cell shape and volume exclusion, and population-level partial differential equation models. We work in an exclusion process framework, considering aligned, elongated cells that may occupy more than one lattice site, in order to represent populations of agents with different sizes. Three different idealisations of the individual-level mechanism are proposed, and these are connected to three different partial differential equations, each with a different diffusion coefficient; one linear, one nonlinear and degenerate and one nonlinear and nondegenerate. We test the ability of these three models to predict the population-level response of a cell spreading problem for both proliferative and nonproliferative cases. We also explore the potential of our models to predict long time travelling wave invasion rates and extend our results to two-dimensional spreading and invasion. Our results show that each model can accurately predict density data for nonproliferative systems, but that only one does so for proliferative systems. Hence great care must be taken to predict density data with varying cell shape
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